Bilinear interpolation

In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables (e.g., x and y) on a rectilinear 2D grid. In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables (e.g., x and y) on a rectilinear 2D grid. The key idea is to perform linear interpolation first in one direction, and then again in the other direction. Although each step is linear in the sampled values and in the position, the interpolation as a whole is not linear but rather quadratic in the sample location. Suppose that we want to find the value of the unknown function f at the point (x, y). It is assumed that we know the value of f at the four points Q11 = (x1, y1), Q12 = (x1, y2), Q21 = (x2, y1), and Q22 = (x2, y2). We first do linear interpolation in the x-direction. This yields We proceed by interpolating in the y-direction to obtain the desired estimate: Note that we will arrive at the same result if the interpolation is done first along the y direction and then along the x direction.